What is ((6^{n+1}*3^{3-n}*2^{1-n}))/((4*9^3)) ?

The solution to ((6^{n+1}*3^{3-n}*2^{1-n}))/((4*9^3)) is 1/9

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simplify ((6^{n+1}3^{3-n}2^{1-n}))/((4*9^3))

simplify

\frac{( 6 ^{n + 1} \cdot 3 ^{3 - n} \cdot 2 ^{1 - n} )}{( 4 \cdot 9 ^{3} )}

\frac{1}{9}

Decimal Notation

0.11111 \dots

Solution steps

\frac{6 ^{n + 1} \cdot 3 ^{3 - n} \cdot 2 ^{1 - n}}{4 \cdot 9 ^{3}}

Factor

6^{n + 1} : 2^{n + 1} \cdot 3^{n + 1}

= \frac{2 ^{n + 1} \cdot 3 ^{n + 1} \cdot 3 ^{3 - n} \cdot 2 ^{1 - n}}{4 \cdot 9 ^{3}}

Factor the number:

4 = 2^{2}

= \frac{2 ^{n + 1} \cdot 3 ^{n + 1} \cdot 3 ^{3 - n} \cdot 2 ^{1 - n}}{2 ^{2} \cdot 9 ^{3}}

Simplify

\frac{2 ^{n + 1}}{2 ^{2}} : 2^{n - 1}

= \frac{2 ^{n - 1} \cdot 3 ^{n + 1} \cdot 3 ^{3 - n} \cdot 2 ^{1 - n}}{9 ^{3}}

Factor

9^{3} : 3^{6}

= \frac{2 ^{n - 1} \cdot 3 ^{n + 1} \cdot 3 ^{3 - n} \cdot 2 ^{1 - n}}{3 ^{6}}

Simplify

\frac{3 ^{n + 1}}{3 ^{6}} : 3^{n - 5}

= 2^{n - 1} \cdot 3^{n - 5} \cdot 3^{3 - n} \cdot 2^{1 - n}

Simplify

2^{n - 1} \cdot 3^{n - 5} \cdot 3^{3 - n} \cdot 2^{1 - n} : \frac{1}{9}

= \frac{1}{9}

\frac{( x ^{2} - 4 x + 3 )}{( x ^{2} - 6 x + 9 )}

(8 x^{5} \cdot y^{3})^{2}

(3 x^{- 3} y^{3})^{- 2}

4 x^{2} + 32 x y + 4 y^{2}

(2 x - 2 y + 2)^{3}

What is ((6^{n+1}*3^{3-n}*2^{1-n}))/((4*9^3)) ?
The solution to ((6^{n+1}*3^{3-n}*2^{1-n}))/((4*9^3)) is 1/9